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Simplifying 4x2 + -21x + 25 = 0 Reorder the terms: 25 + -21x + 4x2 = 0 Solving 25 + -21x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + -5.25x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -5.25x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -5.25x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -5.25x + x2 = 0 + -6.25 -5.25x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -5.25x + x2 = -6.25 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -6.25 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -6.25 + 6.890625 Combine like terms: -6.25 + 6.890625 = 0.640625 6.890625 + -5.25x + x2 = 0.640625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + -2.625) equal to 0.80039053 and -0.80039053.Subproblem 1
x + -2.625 = 0.80039053 Simplifying x + -2.625 = 0.80039053 Reorder the terms: -2.625 + x = 0.80039053 Solving -2.625 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 0.80039053 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 0.80039053 + 2.625 x = 0.80039053 + 2.625 Combine like terms: 0.80039053 + 2.625 = 3.42539053 x = 3.42539053 Simplifying x = 3.42539053Subproblem 2
x + -2.625 = -0.80039053 Simplifying x + -2.625 = -0.80039053 Reorder the terms: -2.625 + x = -0.80039053 Solving -2.625 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -0.80039053 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -0.80039053 + 2.625 x = -0.80039053 + 2.625 Combine like terms: -0.80039053 + 2.625 = 1.82460947 x = 1.82460947 Simplifying x = 1.82460947Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.42539053, 1.82460947}
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